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Power system inertia is declining and is increasingly variable and uncertain in regions where the penetration of non-synchronous generation and interconnectors is growing. This presents a challenge to power system operators who must take appropriate actions to ensure the stability and security of power systems relying on short-term forecasts of the system’s inertial response. Existing models to forecast inertia fail to quantify uncertainty, which may prevent their utilization given the risk aversion of the system operators when handling stability issues. This paper is the first to develop a model to produce calibrated, data-driven probabilistic forecasts of the inertia contribution of transmission-connected synchronous generators. The model provides a necessary tool for system operators to quantify forecast uncertainty, allowing them to manage the risk of frequency instability cost-effectively. The paper demonstrates that the assumption of a Gaussian distribution of uncertainty applied in existing models is not acceptable to accurately forecast the inertial response and provides a satisfactory forecast model by combining non-parametric density forecasting with parametric tail distributions. Moreover, the paper shows that satisfactory predictive performance can only be achieved by adopting a rolling horizon forecast approach to deal with the rapidly changing characteristics of the inertial response in power systems. [ABSTRACT FROM AUTHOR]

Transient stability of a power system can be significantly affected by wind power generators due to their stochastic power output and complex dynamic characteristics. This paper proposes a robust optimization approach for coordinating generation dispatch and emergency load shedding against transient instability under uncertain wind power output. The problem is modelled as a two-stage robust optimization (TSRO) model considering transient stability constraints, where the first-stage is to optimize the generation dispatch (preventive control) before a contingency and the second-stage decision is the emergency load shedding (emergency control) after the contingency occurrence under the worst case of wind power variation. To solve this TSRO problem, this paper also proposes a solution algorithm which integrates transient stability assessment and transient stability constraint construction in a column and constraint generation framework. The proposed method is validated on the New-England 39-bus system and the Nordic32 system, which shows high computational efficiency and stability robustness against uncertain wind power. [ABSTRACT FROM AUTHOR]

A suitable probabilistic scenario set of load demand and natural characteristics of renewable energy is becoming a crucial issue in power system planning studies. Properly addressing the impact of potentially thousands of residential PV plants on the resilience and reliability needs of substations necessitates the representation of inherent relations between photovoltaics and the load throughout the long-term planning period. The optimal planning of substation expansions is achievable through proper modeling of input parameters which describes the characteristics of the service areas. In this paper, the co-existence of PV plants and the load in a service area under three different states such as daytime with clear-sky and no-fault, daytime with abnormal events, and nighttime are incorporated into the stochastic dynamic optimization problem by using scenario-based approach. The scenario tree of the problem is branched from three different bases simultaneously instead of only one as in conventional approach. This paper also combines the risk-constrained stochastic dynamic SEP problem and Mixed Integer Linear Programming (MILP) framework under one roof. The comparison between integrating inherent characteristics of PV plants with and without considering abnormal events into the optimization is performed to show the impact of suitable probabilistic model on dynamic nature of investment decisions. [ABSTRACT FROM AUTHOR]

The integration of the variable renewable energies makes the operation conditions of the power system ever-changeable. Consequently, the power system operational reliability evaluation is increasingly important. This paper introduces the concept of decision-dependent uncertainty (DDU) in the operational reliability evaluation. Unlike the exogenous uncertainties, DDU reveals that the decisions of the system operation could significantly affect the resolution of the uncertainties which influence the reliability metrics. In this paper, the proposed DDU modeling method links the device reliability indices, i.e., the forced outage rate, and the operational-decision variables. The impacts of DDU on operational reliability are analyzed based on a reliability-constrained stochastic unit commitment (UC) model. An adaptive reliability improvement UC (ARIUC) algorithm is proposed to efficiently solve the problem. Case studies underline the necessity of considering DDU in power system operational reliability evaluations. [ABSTRACT FROM AUTHOR]

This paper presents a distributionally robust network-constrained unit commitment (DR-NCUC) model considering AC network modeling and uncertainties of demands and renewable productions. The proposed model characterizes uncertain parameters using a data-driven ambiguity set constructed by training samples. The non-convex AC power flow equations are approximated by convex quadratic and McCormick relaxations. Since the proposed min-max-min DR-NCUC problem cannot be solved directly by available solvers, a new decomposition algorithm with proof of convergence is reported in this paper. The master problem of this algorithm is solved using both primal and dual cuts, while the max-min sub-problem is solved using the primal-dual hybrid gradient method, obviating the need for using duality theory. Also, an active set strategy is proposed to enhance the tractability of the decomposition algorithm by ignoring the subset of inactive constraints. The proposed model is applied to a 6-bus test system and the IEEE 118-bus test system under different conditions. These case studies illustrate the performance of the proposed DR-NCUC model to characterize uncertainties and the superiority of the proposed decomposition algorithm over other decomposition approaches using either primal or dual cuts. [ABSTRACT FROM AUTHOR]

Voltage source converter (VSC) based multi -terminal HVDC (VSC-MTDC) systems have emerged as flexible collector systems for multi-area interconnected AC/DC hybrid grids with high share of volatile renewables energy. However, it remains an open question as how to exploit the flexible and cooperative regulation of multiple VSC stations and enhance secure operation on the premise of information privacy protection of multiple independent dispatch areas. This paper proposed an Analytical Target Cascading (ATC)-based three-layer decentralized optimization approach on flexible operation of VSC-MTDC hybrid systems. The low layer is a chance-constrained stochastic optimal power flow (SOPF) problem for AC grids. To guard against the secure operation risk by a VSC's random unipolar atresia fault, a modified loss of load probability index (MLOLP) is proposed to improve the day-ahead generation-reserve scheme. The middle layer and the high layer are a multiperiod OPF problem for VSC stations and the MTDC grid, respectively, where a detailed power regulation model is built to fully exert the flexible cooperation of multiple VSC stations. Two case systems are tested to verify the effectiveness and superiority of the proposed flexible operation hierarchy. [ABSTRACT FROM AUTHOR]

As power systems are undergoing a significant transformation with more uncertainties, less inertia and closer to operation limits, there is increasing risk of large outages. Thus, there is an imperative need to enhance grid emergency control to maintain system reliability and security. Towards this end, great progress has been made in developing deep reinforcement learning (DRL) based grid control solutions in recent years. However, existing DRL-based solutions have two main limitations: 1) they cannot handle well with a wide range of grid operation conditions, system parameters, and contingencies; 2) they generally lack the ability to fast adapt to new grid operation conditions, system parameters, and contingencies, limiting their applicability for real-world applications. In this paper, we mitigate these limitations by developing a novel deep meta-reinforcement learning (DMRL) algorithm. The DMRL combines the meta strategy optimization together with DRL, and trains policies modulated by a latent space that can quickly adapt to new scenarios. We test the developed DMRL algorithm on the IEEE 300-bus system. We demonstrate fast adaptation of the meta-trained DRL polices with latent variables to new operating conditions and scenarios using the proposed method, which achieves superior performance compared to the state-of-the-art DRL and model predictive control (MPC) methods. [ABSTRACT FROM AUTHOR]

Network reconfiguration (NR) has attracted much attention due to its ability to convert conventional distribution networks (DNs) into self-healing grids. This paper proposes a new strategy for real-time voltage regulation (VR) in a reconfigurable DN, whereby optimal feedforward control of distributed generators (DGs) is achieved in coordination with the operation of line switches (SWs). This enables preemptive compensation of upcoming deviations in DN voltages resulting from NR-aided load restoration. A robust optimization problem is formulated using a dynamic analytical model of NR to design the feedforward voltage controllers (FVCs) that minimize voltage deviations with respect to the H∞ norm. Errors in the estimates of DG modeling parameters and load demands are reflected in the design of optimal FVCs via polytopic uncertainty modeling. Small-signal analysis and case studies are conducted, verifying the effectiveness and robustness of the optimal FVCs in improving real-time VR when NR is activated for load restoration. The performance of the proposed FVCs is confirmed under various conditions of a self-healing DN,characterized by network islanding and size, parameter errors, SW operations, and communication time delays. [ABSTRACT FROM AUTHOR]

Transmission system operators (TSOs) in recent years have faced challenges in order to ensure maximum transmission capacity of the system to satisfy market needs, while maintaining operational safety and permissible impact on the environment. A great help in the decision-making process was introduced with the Dynamic Thermal Rating (DTR) – an instrument to monitor and predict the maximal allowed ampacity of the power grid based on weather measurements and forecast. However, the introduction of DTR raises a number of questions related to the accuracy and uncertainty of the results of thermal assessment and the level of acceptable risk and its management. In this paper, we present a solution for estimating DTR uncertainty, appropriate for operational use at TSOs. With the help of conductor surface temperature measurements, weather measurements and predicted weather data, we also estimate the error of the weather forecast and the DTR itself. Following the results of the data analyses, we build an operative solution for estimating the ampacity uncertainty based on Monte Carlo random simulations and integrate it into the operational environment of ELES – the operator of the Slovenian electric power transmission network. [ABSTRACT FROM AUTHOR]

This paper proposes a novel stochastic robust real-time power dispatch model considering wind uncertainty. In this dispatch model that incorporates automatic power generation control, system constraints are constructed with affinely adjustable robust optimization to enhance the system security, while the objective concerning the expected value of generation cost is optimized to improve the cost efficiency. The optimized objective is consistent with stochastic optimization, while the formulation for the objective is different. A Nataf conversion-based three-point estimate (NC-TPE) is adopted, which uses an approximating function to formulate the expected generation cost with deterministic estimate points. Compared to traditional stochastic sampling methods, the deterministic assessment method NC-TPE achieves an accurate formulation with more stable and efficient computation performance. The dispatch model is derived as a problem with nonconvex objective and bilinear constraints using the dual theory. To address the highly nonconvex problem, the objective and bilinear constraints are first converted to difference-of-convexity functions, and then a tailored difference-of-convexity optimization is employed to convexify the nonconvex functions, such that the original problem can be solved with an iterative quadratically constrained program. Numerical simulations demonstrate the economic superiority and robustness of the proposed model, as well as the effectiveness of the convexified solution. [ABSTRACT FROM AUTHOR]

Pricing multi-interval economic dispatch of electric power under operational uncertainty is considered in this two-part paper. Part I investigates dispatch-following incentives of profit-maximizing generators and shows that, under mild conditions, no uniform-pricing scheme for the rolling-window economic dispatch provides dispatch-following incentives that avoid discriminative out-of-the-market uplifts. A nonuniform pricing mechanism, referred to as the temporal locational marginal pricing (TLMP), is proposed. As an extension of the standard locational marginal pricing (LMP), TLMP takes into account both generation and ramping-induced opportunity costs. It eliminates the need for the out-of-the-market uplifts and guarantees full dispatch-following incentives regardless of the accuracy of the demand forecasts used in the dispatch. It is also shown that, under TLMP, a price-taking market participant has incentives to bid truthfully with its marginal cost of generation. Part II of the paper extends the theoretical results developed in Part I to more general network settings. It investigates a broader set of performance measures, including the incentives of the truthful revelation of ramping limits, revenue adequacy of the operator, consumer payments, generator profits, and price volatility under the rolling-window dispatch model with demand forecast errors. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive scheduling framework for residential demand response (DR) programs considering both the day-ahead and real-time electricity markets. In the first stage, residential customers determine the operating status of their responsive devices such as heating, ventilation, and air conditioning (HVAC) systems and electric water heaters (EWHs), while the distribution system operator (DSO) computes the amount of electricity to be purchased in the day-ahead electricity market. In the second stage, the DSO purchases insufficient (or sells surplus) electricity in the real-time electricity market to maintain the supply-demand balance. Due to its computational complexity and data privacy issues, the proposed model cannot be directly solved in a centralized manner, especially with a large number of uncertain scenarios. Therefore, this paper proposes a combination of stochastic programming (SP) and the alternating direction method of multipliers (ADMM) algorithm, called SP-ADMM, to decompose the original model and then solve each sub-problem in a distributed manner while considering multiple uncertain scenarios. The simulation study is performed on the IEEE 33-bus system including 121 residential houses. The results demonstrate the effectiveness of the proposed approach for large-scale residential DR applications under weather and consumer uncertainties. [ABSTRACT FROM AUTHOR]

Service restoration is one of the critical functions to enable the future self-healing distribution system. To restore the distribution system in a timely and reliable manner, the realistic system operating conditions need to be accurately characterized. In this paper, two main factors that have great impacts on distribution system restoration (DSR) in practice are investigated. First, cold load pickup (CLPU), generally caused by thermostatically controlled loads (TCLs), is a common phenomenon after an outage and shaped by the outage duration. However, the time-dependent behaviors of CLPU are rarely considered in literature. In this paper, the operating state evolution of TCLs after an outage is analyzed to characterize time-dependent CLPU. And the time-dependent CLPU is analytically embedded in DSR to accurately represent the actual behaviors of the restored loads. Second, it is difficult to predict loads that fluctuate during DSR due to the lack of real-time measurement data. Accordingly, a robust DSR based on the information gap decision theory (IGDT) is proposed to address this challenge, fully considering the uncertainty of CLPU. The proposed models are tested in IEEE 13-node and 123-node test feeders. Simulation results demonstrate that the time-dependent CLPU model and the uncertainty modeling of CLPU can accurately capture the actual behaviors of loads with TCLs after an outage, which greatly improves DSR decisions in practice. [ABSTRACT FROM AUTHOR]

This paper presents a multi-period active distribution network planning (ADNP) with distributed generation (DG). The objective of the proposed ADNP is to minimize the total planning cost, subject to both investment and operation constraints. The paper proposes a multi-stage stochastic optimization model to address DG uncertainties over several periods, in which the decisions are made sequentially by only using the present-stage information. A nested decomposition method is proposed which applies the stochastic dual dynamic integer programming (SDDIP) method to address computational intractabilities of the proposed ADNP approach. The presented numerical results and discussions on a 33-bus distribution system and a large-scale 906-bus system verify the effectiveness of the proposed ADNP method and its solution method. [ABSTRACT FROM AUTHOR]

The modern photovoltaic inverter has an active power-reactive power (Watt-VAr) control curve that is part of its management modes. The Watt-VAr curve, whose settings can be remotely modified, regulates the inverter reactive power output in function of its active power. This paper proposes the optimization of inverter segregated linear decision rules (LDRs), starting from the legacy Volt-VAr optimization in distribution networks. As opposed to classical LDRs that are interfaced with Volt-VAr optimization, the segregated LDRs are piecewise linear continuous curves that directly satisfy the reactive power capability of inverters, and their multiple segments can capture the correlation in solar power variability. The paper presents linear programming formulations for optimizing the segregated linear decision rules using stochastic optimization, robust optimization, and distributionally robust optimization. The optimization schemes are demonstrated on both meshed and radial networks, and their performance is validated via Monte-Carlo simulation. [ABSTRACT FROM AUTHOR]

In this paper, we propose a data-driven approach for uncertainty moment propagation through the non-linear power system dynamics. The proposed approach relies on the linear representation of a nonlinear system using the Perron-Frobenius & Koopman operators for propagating the moments. Data from non-linear simulations is used to approximate the linear operators by matrices, thereby enabling moment propagation by matrix multiplication. Results for a large-scale system are presented to demonstrate the accuracy and speed-up of the proposed method. [ABSTRACT FROM AUTHOR]

Renewable generation has grown rapidly these years due to its advantages in low environmental impacts. Stand-alone microgrid with renewable generation and energy storage is a promising option in remote areas beyond the reach of an existing power grid. This paper proposes a multiobjective optimization model to co-optimize the sizes of renewable generation and energy storage in stand-alone microgrids, which minimizes the load shedding risk and the total investment cost. The load shedding degree is obtained by an optimal operation problem and measured by shortfall risk, considering the uncertainties of demand and renewable resources. To deal with the inaccurate empirical distribution, distributionally robust shortfall risk is further established under a Wasserstein-metric-based ambiguity set, and an equivalent distributionally robust formulation is obtained. Then a conservative approximation is developed, and the resulting problem appears to be a bi-objective linear program. The Pareto frontier is proven to be piecewise linear, and the analytical expression of the Pareto frontier is derived. Case studies demonstrate the effectiveness and performance of the proposed method. [ABSTRACT FROM AUTHOR]

This paper exploits the decomposition structure of the large-scale hydrothermal generation expansion planning problem with an integrated modified Benders Decomposition and Progressive Hedging approach. We consider detailed and realistic data from the Brazilian power system to represent hourly chronological constraints based on typical days per month and year. Also, we represent the multistage stochastic nature of the optimal hydrothermal operational policy through co-optimized linear decision rules for individual reservoirs. Therefore, we ensure investment decisions compatible with a nonanticipative (implementable) operational policy. To solve the large-scale optimization problem, we propose an improved Benders Decomposition method with multiple instances of the master problem, each of which strengthened by primal cuts and new Benders cuts generated by each master’s trial solution. Additionally, our new approach allows using Progressive Hedging penalization terms for accelerating the convergence of the method. We show that our method is 60% faster than the benchmark. Finally, the consideration of a nonanticipative operational policy can save 7.64% of the total cost (16.18% of the investment costs) and significantly improve spot price profiles. [ABSTRACT FROM AUTHOR]

This paper proposes a market framework to approach economic dispatch as a subproblem in smart distribution systems. Four subproblems are associated with four different submarkets (SMs) in the presented framework. Market participants are eligible to bid in different submarkets based on the type of their distributed generation (DG) unit. To effectively tackle the conflicts among objective functions of different submarkets, the corresponding formulated subproblems are assigned to two different agents, namely distribution system operator (DSO) and a green bank agent (GBA). A communication mechanism is designed within the proposed framework such that DSO and GBA compromise their solutions and find a tradeoff to reasonably address the concerns of the four subproblems within SMs 1-4. The effectiveness of the proposed market framework is validated on a well-known 136-bus distribution system, which is modified to contain wind turbine DG aggregators, photovoltaic DG aggregators, and diesel-engine DG aggregators. [ABSTRACT FROM AUTHOR]

Energy sharing has the potential to decrease operation costs by exploiting the complementarity of different entities. The further increase of microgrids’ generation capacity in the distribution network could trigger the emergence of MW-level microgrids aggregator (MGA) to participate in the regional energy sharing market (ESM) and sell excess energy. However, the uncertainty of renewable energy generation will cause the failure of energy sharing and an economic loss for the energy sharing market. Therefore, a novel two-sided market with the clearing price and risk management is proposed in this paper. In order to optimize the energy sharing strategy of MGAs, a network-constrained risk-averse two-stage stochastic game model based on DC optimal power flow (OPF) is established. The objective of the MGA is to maximize the revenue in the ESM while the subtransmission network operator (SNO) aims to achieve regional energy self-sufficiency. The sample average approximation (SAA) method is employed to approximate the stochastic Cournot-Nash equilibrium. A distributed market clearing algorithm based on the alternating direction method of multipliers (ADMM) and best response seeking is developed to solve the optimal bidding problem of MGAs and the optimal dispatch problem of the SNO. Furthermore, the existence of the SAA Nash equilibrium is also investigated. Numerical simulations prove that the proposed game model can effectively control the overbidding risk and promote regional energy self-sufficiency. [ABSTRACT FROM AUTHOR]

Unit Commitment (UC) is an important problem in power system operations. It is traditionally planned for 24 hours with one-hour time intervals. To accommodate the increasing net-load variability, sub-hourly UC has been suggested for improved system flexibility. Such a problem is larger and more complicated than hourly UC because of the increased number of periods and reduced unit ramping capabilities per period. The computational burden is further exacerbated for systems with large numbers of virtual transactions leading to dense transmission constraint matrices. Consequently, the state-of-the-art and practice method, branch-and-cut (B&C), suffers from poor performance. In this paper, our recent Surrogate Absolute-Value Lagrangian Relaxation (SAVLR) is enhanced by embedding ordinal-optimization concepts for a drastic reduction in subproblem solving time. Rather than formally solving subproblems by using B&C, subproblem solutions satisfying SAVLR's convergence condition are obtained by modifying solutions from previous iterations or solving crude subproblems. All virtual transactions are included in each subproblem to reduce major changes in solutions across iterations. A parallel version is also developed to further reduce the computation time. Testing on MISO's large cases demonstrates that our ordinal-optimization embedded approach obtains near-optimal solutions efficiently, is robust, and provides a new way of solving other MILP problems. [ABSTRACT FROM AUTHOR]

The design of electricity imbalance pricing mechanisms is internationally controversial. Policies on whether to permit virtual trading for market participants and whether, or how, to impose penalty incentives on the imbalance volumes vary widely. Furthermore, market designs vary depending whether the imbalance prices are obtained directly from real-time trading or based upon the offer and demand functions from the day-ahead energy markets. This paper develops an analytical framework for evaluating designs for imbalance settlement mechanisms and we have selected the Japanese electricity market, which has undergone several revisions in its imbalance mechanism, as a good example to assess such variations. We develop a predictive approach for the imbalance volumes and price densities using two-step quantile regressions and derive a new trading optimization for a virtual trader's arbitrage position. We construct supporting models to estimate prediction errors for renewable power and demand as drivers of imbalance volume. The empirical analysis reveals that even in a mechanism with imbalance penalties based upon day-ahead reference prices, virtual trading may still be beneficial to market participants as well as to the system operator. We also find that greater market transparency is crucial for increased benefits. The insights generalize beyond the Japan case study. [ABSTRACT FROM AUTHOR]

Microgrid's voltage regulation is of particular importance during both grid-connected and islanded modes of operation. Especially, during the islanded mode, when the support from the upstream grid is lost, stable voltage regulation is vital for the reliable operation of critical loads. This paper proposes a robust and data-driven control approach for secondary voltage control of AC microgrids in the presence of uncertainties. To this end, unfalsified adaptive control (UAC) is utilized to select the best stabilizing controller from a set of pre-designed controllers with the minimum knowledge required from the microgrid. Two microgrid test systems are simulated in MATLAB to verify the effectiveness of the proposed method under different scenarios like load change and communication link failure. [ABSTRACT FROM AUTHOR]

Midcontinent Independent System Operator (MISO) plans to introduce 30-minute short-term reserve (STR) to address 30 minutes system flexibility needs. Transmission bottlenecks in the power system may inhibit the deliverability of STR. Insufficient deliverable reserve may require additional operator manual adjustments, which may be uneconomic and distort the market price signal. To improve reserve deliverability, event-based zonal STR clearing model and nodal STR clearing model are proposed to distribute reserve across the grid. This paper compares reserve deliverability and market clearing prices between the zonal STR model and the nodal STR model. A new design on penalty function is proposed in this paper to reflect the true value of security constraints for reserve deployment with the consideration of multiple events. Analysis of MISO test cases shows that the zonal approach is imprecise and may not guarantee the actual post-event flows within the physical limits. Nodal STR model can improve the reserve deliverability, market efficiency, and price signal. [ABSTRACT FROM AUTHOR]

This paper presents a new framework for multistage expansion planning in active power distribution networks, in which the distribution system operator (DSO) considers active network management by clearing the local energy market at the distribution level. The proposed model is formulated as a bi-level optimization problem, where the upper level minimizes the net present value of the total costs imposed to DSO associated with the investment and maintenance of the network assets as well as the network operation, while the lower level on clearing the local energy market captures the participation of distributed energy resource (DER) owners and demand aggregators to maximize the social welfare. The expansion plans consider the investments in DER owners’ assets as well as variety of network assets in which the profitability of DER owners’ investment is guaranteed. The Karush-Kuhn-Tucker optimality conditions and the strong duality theory are employed through which the model is converted to a mixed integer linear programming optimization problem. The implementation of the suggested model on the 24-bus and 86-bus distribution test systems validates its performance and efficacy in making cost-effective planning decisions. [ABSTRACT FROM AUTHOR]

Block orders are increasingly adopted in many electricity markets as they enable power producers to implicitly express their unit commitment characteristics and address price volatility risks. However, previous work on the optimal offering problem of a price-taking producer participating in such markets has only considered the simplest type of block orders (regular block orders-RBO) and has neglected relevant realistic market regulations. This paper addresses these simplifications by proposing a new optimal offering model which also considers the more complex profile block orders (PBO) and linked block orders (LBO). This model is generic in that it can treat the block orders’ time spans either as fixed parameters (following the modelling approach of previous work) or as endogenous decision variables, which constitutes a completely novel modeling approach. The presented case studies demonstrate that this novel approach yields a tremendously lower number of binary variables and more efficient computational performance, when PBO and LBO are considered. Furthermore, the case studies analyze the physical conditions under which the introduction of different types of block orders increases the examined producer’s profit. [ABSTRACT FROM AUTHOR]

As an efficient tool for uncertainty quantification of renewable energy forecasting, prediction intervals (PIs) provide essential prognosis to power system operator. Merely improving the statistical quality of PIs with respect to calibration and sharpness cannot always contribute to the operational value for specific decision-making issue. In this paper, the cost-oriented prediction intervals are firstly proposed to achieve the joint improvement of forecasting quality and decision performance. In order to bridge the gap between forecasting and decision, a novel cost-oriented machine learning (COML) framework is established, which unifies nonparametric renewable power PI construction and decision-making. Formulated as a bilevel programming model, the COML minimizes the operational costs of decision-making process by adaptively adjusting the quantile proportion pair of PIs resulting from extreme learning machine based quantile regression. The hierarchical optimization model of the COML is equivalently simplified as a single level nonlinear programming problem. Then an enhanced branch-and-contract algorithm with innovative bounds contraction strategy is devised to efficiently capture the optimum of the single level problem with bilinear nonconvexity. Numerical experiments based on actual wind farm data simulate the online forecasting and decision process for wind power offering. Comprehensive comparisons verify the substantial superiority of the proposed COML methodology in terms of forecasting quality, operational value, as well as computational efficiency for practical application. [ABSTRACT FROM AUTHOR]

This paper proposes a machine learning method for the reliability evaluation of integrated power-gas systems (IPGS) under the uncertain component failure probability distributions. The Random Forest (RF) method is designed to select important features to solve the insufficient quantity of data and the curse of dimensionality problems. The Extreme Gradient Boosting (XGBoost) regression algorithm is developed to quantify the relationship between the uncertain parameters and reliability metrics. Moreover, a ten-fold cross-validation method is employed to further improve the accuracy of the regression model. Simulation results on three test systems show that the proposed method can achieve high accuracy for the reliability evaluation. [ABSTRACT FROM AUTHOR]

Renewable Energy Sources (RESs) integration strengthens the need for a power network that can robustly handle the system’s uncertain scenarios. This paper proposes the first nonlinear novel dual-based bi-level approach for robust AC Transmission Expansion Planning (TEP) with uncertainties in RES generations and loads. It utilizes a convex relaxation and is solved by Benders Decomposition (BD), where the master determines the robust AC expansion plan. The novel dual slave for the second level of BD circumvents the issues in using conventional conic dual theory and aids in the worst-case realization of uncertainties using additional novel constraints. The proposed slave is solved using Interior Point Method (IPM), as it is not a mixed-integer problem. The proposed work includes additional linear constraints to speed up BD’s convergence and direct the master towards optimality. The approach is tested on several transmission systems, including the Indian Northern Regional Power Grid (NRPG) system. The robustness of the obtained plans is verified by Monte-Carlo Simulation (MCS) of the actual nonlinear and nonconvex AC Optimal Power Flow (OPF). The effect of the budget of uncertainty on the AC expansion plan is also investigated. A comparison with two previous works reveals the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

With the increasing penetration of renewable energy, accurate and efficient probabilistic optimal power flow (POPF) calculation becomes more and more important to provide decision support for secure and economic operation of power systems. This paper develops a novel nonparametric probabilistic optimal power flow (N-POPF) model describing the probabilistic information by quantiles, which avoids any parametric probability distribution assumptions of random variables. A novel critical region integral method (CRIM) which combines the multiparametric programming theory and discrete integral is proposed to efficiently solve the N-POPF problem. In the CRIM, the critical region partitioning algorithm is firstly introduced into the POPF model to directly establish the mapping relationship from wind power to optimal solutions of the POPF problem. Besides, a discrete integral method is developed in the CRIM to achieve the probability convolution calculation based on quantiles. Comprehensive numerical experiments verify the superior performance of the proposed CRIM in estimation accuracy and computational efficiency, and demonstrate that N-POPF model significantly improves the accuracy of uncertainty analysis. In general, the proposed N-POPF model and CRIM form a new framework of POPF problem for power system analysis and operation. [ABSTRACT FROM AUTHOR]

Distribution systems are becoming more active and provide more power support for transmission systems via their connection points at the transmission-distribution (T-D) interfaces. This paper proposes a chance constrained optimization model to estimate the flexibility area at a T-D interface. In this model, network flexibility is for the first time involved and facilitated by introducing power flow routers (PFRs) into the distribution system. The chance-constrained flexibility area (CCFA) given by the proposed model provides a description of the aggregated power dispatchability of distribution system with the guarantee of low risks of voltage violations under renewable uncertainties. We exploit the mechanism of network flexibility and reveal that it significantly reduces the voltage standard deviations, which cannot be achieved by node power flexibility. To evaluate the CCFA, an efficient two-layer iteration algorithm is designed. The inner layer finds the boundary point of CCFA along a given direction for active and reactive power. The outer layer determines those key directions to be included in the estimation as the corresponding points capture the features of the CCFA boundary. Case studies show that PFRs significantly enlarge the CCFA, which reveals that network flexibility is an important supplement to node power flexibility in T-D interaction. [ABSTRACT FROM AUTHOR]

This paper proposes a novel modeling framework and decomposition-based solution strategy combining stochastic programming (SP) and robust optimization (RO) to deal with multiplex uncertainties in coordinated mid- and long-term power system planning. The problem is formulated as a multi-year generation and transmission planning problem from an independent system operator (ISO)’s perspective to minimize both expansion and operational costs under binary and continuous uncertainties, ${\bf i.e.}$ , system component contingency and load/generation variation. N- $\bf {k}$ contingencies are captured in RO using the reformulated contingency criteria, while the load/generation uncertainty is considered in SP embedded with RO using operating scenarios generated from the historical data with spatiotemporal correlations. The original hybrid model is highly intractable, but the intractability can be relieved by the proposed decomposition strategy based on the column-and-constraint generation and L-shaped algorithms. We apply our model to perform long-term system planning under extremely high renewable penetration and investigate the case of 100% renewables in long-term planning. Numerical experiments on multi-scale test systems verify the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper develops a computationally efficient algorithm which speeds up the probabilistic power flow (PPF) problem by exploiting the inherently low-rank nature of the voltage profile in electrical power distribution networks. The algorithm is accordingly termed the Accelerated-PPF (APPF), since it can accelerate “any” sampling-based PPF solver. As the APPF runs, it concurrently generates a low-dimensional subspace of orthonormalized solution vectors. This subspace is used to construct and update a reduced order model (ROM) of the full nonlinear system, resulting in a highly efficient simulation for future voltage profiles. When constructing and updating the subspace, the power flow problem must still be solved on the full nonlinear system. In order to accelerate the computation of these solutions, a Neumann expansion of a modified power flow Jacobian is implemented. Applicable when load bus injections are small, this Neumann expansion allows for a considerable speed up of Jacobian system solves during the standard Newton iterations. APPF test results, from experiments run on the full IEEE 8500-node test feeder, are finally presented. [ABSTRACT FROM AUTHOR]

Over the past 20 years, the rapid integration of renewable energy has resulted in electricity markets that are increasingly complex, interconnected, and uncertain. Similar to the banking system's financial crisis in 2008 due to chained reactions, severe financial losses due to uncertainty at a large renewable farm could induce significant financial losses at other market participants. The spread of such financial shocks can be worsened by centralized market clearing, and systemic risks consequently germinate in electricity market operations. Therefore, our previous work has compared systemic risk with systematic risk in the electricity market with uncertainties. However, the scope of our previous work has been limited to risk indices. This paper aims to broaden the study by proposing the theoretical foundation of systemic risk analysis in electricity markets with uncertainties. First, an electricity market financial network is defined to describe the cash inflow/outflow of all participants, and the financial contagion is employed to model the interlinks between different entities. Then, two financial properties, financial resilience and financial reliability, are proposed to evaluate the systemic risk in market settlements with uncertainties. Finally, the proposed theoretical foundation of systemic risk is demonstrated on the Texas synthetic 2000-bus system with 70% renewable penetration. [ABSTRACT FROM AUTHOR]

Uncertainty arising from renewable energy results in considerable challenges in optimal power flow (OPF) analysis. Various chance-constrained approaches are proposed to address the uncertainty within OPF models. However, most existing approaches either assume that the uncertainty distributions are known a priori or consider individual chance constraint modeling. This paper proposes a distributionally robust (DR) joint chance-constrained OPF model, which ensures that the operational constraints are simultaneously satisfied with a given probability and does not require an assumption of specific probability distributions. An ambiguity set built on the first two moments is used to model the uncertainty. An optimized Bonferroni approximation (OBA) is first introduced to decompose the DR joint chance constraint into DR individual chance constraints. The resulting OBA formulation is strongly nonconvex. Different convex approximations are then proposed to formulate the OBA formulation as tractable forms. The proposed convex approximations can be easily extended to incorporate the structural information associated with uncertainty, and correlations among reserve chance constraints. Case studies demonstrate the effectiveness of the proposed convex approximation methods and their extensions. [ABSTRACT FROM AUTHOR]

Uncertainties in renewable generation make accurate load forecast essential for reliable power system operation. This paper considers energy imbalance market (EIM), where market players are allowed to procure energy ahead of time and trade the mismatch due to forecast error and strategic behaviors. The ISO sets the trading prices according to the market conditions, and pursues various system-level objectives. We first identify the power-law relationship between data volume and forecast accuracy, which enables the formulation of forecast cost model. Then, we cast the interactions in the EIM in the Stackelberg game framework with the ISO acting as the leader. We offer explicit subgame perfect equilibrium among the players in EIM, and derive the sufficient condition for the existence of unique equilibrium. Then, we show that this equilibrium, if exists, supports the maximal social welfare and under certain conditions, minimizes the total mismatch. We further examine the local and global impacts of the forecast errors under mild conditions, together with robustness analysis. Such analysis provides mechanism design guidelines for the ISO to enable the data sharing and forecast method sharing among market players in the EIM. Numerical studies further examine the effectiveness, robustness and sensitivity of the subgame. [ABSTRACT FROM AUTHOR]

This paper proposes a new deep learning (DL) based model-free robust method for bulk system on-line load restoration with high penetration of wind power. Inspired by the iterative calculation of the two-stage robust load restoration model, the deep neural network (DNN) and deep convolutional neural network (CNN) are respectively designed to find the worst-case system condition of a load pickup decision and evaluate the corresponding security. In order to find the optimal result within a limited number of checks, a load pickup checklist generation (LPCG) algorithm is developed to ensure the optimality. Then, the fast robust load restoration strategy acquisition is achieved based on the designed one-line strategy generation (OSG) algorithm. The proposed method finds the optimal result in a model-free way, holds the robustness to handle uncertainties, and provides real-time computation. It can completely replace conventional robust optimization and supports on-line robust load restoration which better satisfies the changeable restoration process. The effectiveness of the proposed method is validated using the IEEE 30-bus system and the IEEE 118-bus system, showing high computational efficiency and considerable accuracy. [ABSTRACT FROM AUTHOR]

Few studies have focused on assessing the transient and steady-state voltage stability status of dynamic systems simultaneously. This motivated us to propose a new concept referred to as joint voltage stability assessment (JVSA). Towards this end, this paper proposes a novel data-driven JVSA method considering load uncertainty. It combines multiple convolutional neural networks (multi-CNNs) and a novel variational Bayes (VB) inference for better JVSA accuracy. First, the multi-CNN model is utilized to fast estimate the maximum voltage deviations during the transient and steady-state process. Uncertain load scenarios and system topology under $N$ -1 contingency with are chosen as inputs of each CNN model. Second, estimated voltage deviations are put into the VB inference to automatically infer the transient and steady-state voltage stability status. To validate its effectiveness, numerical simulations are performed on the modified WECC 179-bus system by comparing with benchmark algorithms. It is demonstrated that the proposed data-driven JVSA method is more accurate and faster than the conventional VSA method. [ABSTRACT FROM AUTHOR]

The output of renewable generation depends on the real-time weather conditions and changes rapidly; so the economic operating point of the power system varies over time. This paper aims to find the explicit mapping from variable renewable power to optimal power flow solutions. To this end, we propose a parametric distribution optimal power flow (P-DOPF) method, which gives the optimal dispatch strategy and power flow status as analytical functions of the renewable output. With the established distribution optimal power flow problem based on the relaxed Distflow model, the first step is to perform a global polyhedral approximation on the second-order cone constraints to develop a linearized formulation. The second step is to obtain the P-DOPF model by treating renewable power output as parameters; then, the P-DOPF problem gives rise to a multi-parametric linear program (mp-LP). Third, we prove that the optimal solution and optimal value of the P-DOPF are piecewise linear functions of the parameters and we design an adaptive-sampling algorithm to construct the optimal value and optimal solution functions, as well as the partition of the parameter set, subject to a given error tolerance; this algorithm is not influenced by model degeneracy, a common difficulty of existing mp-LP algorithms. The P-DOPF framework provides an explicit real-time control policy of generators in response to the renewable output. Case studies on the IEEE 33 and 69-bus systems verify the effectiveness and performance of the proposed method; by comparison, the proposed method outperforms the established affine policy method in computational efficiency and optimality by 24.5% and 4.62%, respectively. [ABSTRACT FROM AUTHOR]

New resource mix, e.g., renewable resources, are imposing operational complexities to modern power systems by intensifying uncertainty and variability in the system net load. This issue has motivated independent system operators (ISOs), e.g., California ISO (CAISO), to add flexible ramping products (FRPs) to their day-ahead (DA) market models. Such structural changes in the DA market formulation require further analyses and detailed design to ensure adequate operational flexibility, market efficiency, and reliability. This paper conducts a comprehensive study to: (a) augment existing DA market models with enhanced FRP design to schedule ramp capabilities that are more adaptive with respect to the real-time (RT) 15-min net load variability and uncertainty, and (b) design corresponding market payment policies that accurately reflect the value of the added flexibility through enhanced FRP design. The proposed FRP design can be implemented in present-day system operations with minimal disruption to existing DA market models. Performance of the proposed DA market model, which includes the enhanced FRP design, is compared against the DA market model with existing FRP design through a validation methodology based on RT unit commitment model. This validation methodology mimics fifteen-minute markets of CAISO. The proposed method is tested on an IEEE 118-bus test system. [ABSTRACT FROM AUTHOR]

Reliable planning of electricity networks is a crucial challenge to maintain the continuous power supply. This can be ensured through careful planning which requires a number of parameters as inputs such as electricity demand, generation capacity, fuel price, renewable intermittent generation, among others. The uncertain behaviors of such parameters have been well studied in literature. Another important parameter which is a vital requirement for reliable planning is the resistance of overhead transmission lines. Traditionally, the current models ignore to consider the resistance variations due to Joule heating and ambient temperature changes in transmission expansion planning (TEP) problem. In this sense, this paper presents an adaptive robust optimization (ARO) framework for TEP to model the uncertain resistance through ellipsoidal uncertainty set. Moreover, a data-driven selection of the ellipsoidal uncertainty set is proposed. In this regard, Khachiyan's algorithm (KA) is used to identify the minimum-volume covering ellipsoid (MVCE) that contains all uncertain parameters. A case study based on IEEE 118-bus power system is presented to demonstrate the effectiveness of the proposed method. Simulation results show that resistance uncertainty is of serious concern in the TEP problem since the solutions are highly sensitive to fluctuations in the line resistances. [ABSTRACT FROM AUTHOR]

A reduced level of system inertia due to renewable integration increases the need for cost-effective provision of ancillary services, such as Frequency Response (FR). In this paper a closed-form solution to the differential equation describing frequency dynamics is proposed, which allows to obtain frequency-security algebraic constraints to be implemented in optimization routines. This is done while considering any finite number of FR services with distinguished characteristics, such as different delivery times and activation delays. The problem defined by these frequency-security constraints can be formulated as a Mixed-Integer Second-Order Cone Program (MISOCP), which can be efficiently handled by off-the-shelf conic optimization solvers. This paper also takes into account the uncertainty in inertia contribution from the demand side by formulating the frequency-security conditions as chance constraints, for which an exact convex reformulation is provided. Finally, case studies highlighting the effectiveness of this frequency-secured formulation are presented. [ABSTRACT FROM AUTHOR]

Stochastic optimization can be used to model predictable but uncertain element failures, in an attempt to enhance system reliability in power system operation and planning. In practical applications, such as preventive operation during severe weather, the uncertainty set is often very large. This will lead to two challenges: (i) every possible scenario cannot be practically identified; and (ii) the computational demands of stochastic optimization with a large scenario set cannot be met. To address these challenges, this paper develops a multidimensional scenario selection method, which creates a rather small but representative set of scenarios. The developed method makes use of failure features as well as network features of the elements that may fail, to achieve a superior performance. The simulations studies on a synthetic large-scale Texas system, show the dominant performance of the method compared to existing algorithms in the literature, as well as common industry practices. Due to its effectiveness, the method presented in this paper enables computationally efficient implementation of stochastic power system operation and planning software tools. Such stochastic tools will improve system reliability and efficiency through enhanced use of the existing resources, without requiring any expensive system upgrade. [ABSTRACT FROM AUTHOR]

The increasing penetrations of renewable energy in the electricity sector and plug-in electric vehicles (PEVs) in the transportation sector have increased the interests in introducing new methods to deal with uncertainties in power system studies. In this paper, a new distributionally robust optimization (DRO) via scenario wise ambiguity set is proposed to develop a collaborative bidding strategy for intermittent resources such as hydroelectric generation, wind farms, solar farms and electric vehicle aggregator in the day-ahead energy market. The proposed scenario wise ambiguity set is based on Wasserstein distance and is capable of considering both distributional information and statistical distance metric information in the ambiguity set. In this context, the robust counterpart of proposed DRO applying scenario based affine recourse approximation is developed in this paper. The proposed methodology is applied on a 3-bus test system as well as IEEE 118-bus test system to corroborate the effectiveness of the novel DRO model. [ABSTRACT FROM AUTHOR]

The utilization of aggregated demand-side flexibility via demand response (DR) has become a promising pathway for the integration of renewable energy resources in power systems. Nowadays, there are several management strategies for DR such as the price-based transactive control strategies. However, many of such existing price-based control strategies neglect the physics and operational constraints of the underlying distribution networks when computing the price, raising concerns regarding their theoretical and practical values. This paper studies this issue and investigates optimal DR (ODR) by incorporating the distribution locational marginal price (DLMP). In particular, we discuss DR in connection with DLMPs and propose a multi-period bilevel optimization problem to find the ODR strategy. The objective is to minimize the peak load, load fluctuation, and payments of load aggregators. In addition, a robust bilevel ODR model is formulated to provide a robust ODR strategy while minimizing operating costs under the worst-case realization of uncertainties; this mitigates the impact of forecasting errors on renewable energy resources. Then, we propose an efficient solution approach by employing the Karush-Kuhn-Tucker conditions and strong duality. Simulation results are presented to illustrate the mutual impacts of the interaction between DR and DLMP and the benefits of the robust ODR strategy. [ABSTRACT FROM AUTHOR]

Electricity market participants rely on data-driven methods using public market data to predict locational marginal prices (LMPs) and determine optimal bidding strategies, since they cannot access confidential power system models and operating details. In this paper, system-wide heterogeneous public market data are organized into a 3-dimensional (3D) tensor, which can store their spatio-temporal correlations. A generative adversarial network (GAN)-based approach is proposed to predict real-time locational marginal prices (RTLMPs) by learning the spatio-temporal correlations stored in the historical market data tensor. An autoregressive moving average (ARMA) calibration method is adopted to improve the prediction accuracy. Case studies using public market data from Midcontinent Independent System Operator (MISO) and Southwest Power Pool (SPP) demonstrate that the proposed method is able to learn spatio-temporal correlations among RTLMPs and perform accurate RTLMP prediction. [ABSTRACT FROM AUTHOR]

Virtual power plant (VPP) provides a flexible solution to distributed energy resources integration by aggregating renewable generation units, conventional power plants, energy storages, and flexible demands. This paper proposes a novel stochastic adaptive robust optimization (SARO) model for determining the optimal self-scheduling plan for VPP’s participation in the day-ahead energy-reserve market. We consider exogenous uncertainties (or called decision-independent uncertainties, DIUs) associated with market clearing prices and available wind generation, as well as endogenous uncertainties (or called decision-dependent uncertainties, DDUs) pertaining to real-time reserve deployment requests. A tractable solution methodology based on modified Benders dual decomposition is developed to effectively solve the proposed SARO model with both DIUs and DDUs. Case studies are conducted to verify the efficiency and applicability of the proposed approach. Comparative results show that the proposed method can mitigate the conservatism of robust strategy by capturing a satisfactory trade-off between profitability and real-time operation feasibility. [ABSTRACT FROM AUTHOR]

As the installation of electronically interconnected renewable energy resources grows rapidly in power systems, system frequency maintenance and control become challenging problems to maintain the system reliability in bulk power systems. As two of the most important frequency control actions in the control centers of independent system operators (ISOs) and utilities, the interaction between Economic Dispatch (ED) and Automatic Generation Control (AGC) attracts more and more attention. In this paper, we propose a robust optimization based framework to measure the system flexibility by considering the interaction between two hierarchical processes (i.e., ED and AGC). We propose a cutting plane algorithm with the reformulation technique to obtain seven different indices of the system. In addition, we study the impacts of several system factors (i.e., the budget of operational cost, ramping capability, and transmission line capacity) and show numerically how these factors can influence the system flexibility. [ABSTRACT FROM AUTHOR]

This paper considers an event-triggered mechanism (ETM) for multiple frequency services of electric vehicles (EVs) in smart grids (SGs). A new model of a SG with an ETM and multiple agents of EVs is introduced. ETM is deployed to reduce the load on network bandwidth. EVs are incorporated in both secondary and primary frequency services to suppress frequency fluctuations in the system. The behaviours of EV owners are also considered by using batteries SOC controls. Then, a mathematical model of the system is derived which contains parametric uncertainties due to the incorporation of SOC control, an ETM variable arising from ETM control, and a time-varying delay in both the state and control input vectors. We derive new Lyapunov stability and stabilizability conditions to ensure robust $H_{\infty }$ performance of the closed-loop system. The conditions are derived based on various mathematical tools including relaxed Jensen inequality, free weighting matrix technique, reciprocally convex approach, and matrix inequality for uncertainties. An effective procedure is proposed based on an approach using the state transformation and tractable linear matrix inequalities to synthesis robust static output feedback controller gains. Extensive simulations of a SG with three agents of EVs are undertaken to validate of our proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper presents a new algorithm based on the partial least square (PLS) techniques and the arbitrary polynomial chaos expansion (aPCE) for the probabilistic power flow (PPF) analysis of a power system having many uncertain variables. The proposed method uses the nonlinear PLS to transform a set of random input variables to a smaller number of de-correlated random variables. Then, the aPCE technique is applied to generate the basis polynomial functions and build a surrogate model of the power system response. The algorithm has been implemented and tested with the modified IEEE 118-bus and European 1354-bus systems. The numerical results indicate that, similar to the sparse PCE method and the low-rank approximation technique, the proposed method can be applied to high-dimensional PPF problems. Nonetheless, the proposed approach uses smaller computation time, and estimates statistical characteristics of the response with higher accuracy. [ABSTRACT FROM AUTHOR]